You did the right thing by getting pre-approved with your credit union. But let's not put the cart before the horse.
First, if the car is not a certified used car, you will need to have a pre-purchase inspection performed by a mechanic of your choice + a carfax to see if its really worth buying at any cost.
Only after you have the mechanic's report and estimate will you be ready to even initiate negotiations. The price at this point is only an "asking" price - usually grossly inflated for those few poor lost souls who don't know how to buy a car and pay far more than it is worth. Completely ignore the asking price. Pretend it does not even exist and act shocked at the outrageous high price if is stated or shown on the car. If you are a poor negotiator, bring someone with you. I have done this many times for friends and have saved them many, many thousands - in one case close to 5 figures on a luxury brand. In return, I usually get dinner or a few dozen oysters, sometimes a case of wine. If you don't walk out on the negotiations at least once, you will have paid too much.
Once you agree on a price after negotiations (plan on a whole day at least, or a weekend), only then bring up the issue of paying for the car. That is the only time this detail is relevant. Tell the dealer that you are pre-approved at X% (be honest) and give him a chance to beat that rate. You may be surprised. Dealers have multiple relationships with lenders and may beat your credit union rate. I bought 2 new vehicles in 2011 thinking that the dealer would not be able to beat my pre-approved rates of 3.45 and 3.35%. In both cases, the dealer beat the rates (3.24 and 3.25% for 3 years). Keep the term as short as possible to minimize the total amount of interest paid. On a new car, never exceed a term of 48 months (unless the rate is 0%); 36 or 24 months is even better. Remember that the total of all payments is really the out-of-pocket cost of the car, so keep that term as low as possible.
The non-certified used car warranty can also be negotiated. When I have felt that I truly could not get the car for any less, I will consider asking them to double the warranty length. Once you have agreed to the price after a long negotiation, they will feel a moment of victory after dealing with such a worthy adversary. At that moment, it is fairly easy to get this "one last detail" in order to sign the purchase contract.
Its really not that difficult. Remember there are plenty of used cars out there and I cannot emphasize enough that you should not be afraid to walk out in the middle of negotiations, even after you have paid for a mechanic's inspection. Your feet are wonderful negotiators and their fear that you will walk is to your advantage.